[Solved] You are given a list of non-negative integers and need to arrange them to form the largest possible number when... Which algorithmic approach guarantees an optimal solution for this problem? | Greedy Algorithms

Greedy Algorithms - Largest Number (Arrange to Form Biggest)

You are given a list of non-negative integers and need to arrange them to form the largest possible number when concatenated. Which algorithmic approach guarantees an optimal solution for this problem?

ADynamic Programming to find the maximum concatenation by exploring all subsequences

BSorting the numbers as strings using a custom comparator that compares concatenations

CGreedy approach by always picking the largest integer first

DBrute force generating all permutations and selecting the maximum concatenation

Step-by-Step Solution

Solution:

Step 1: Understand the problem requires ordering numbers to maximize concatenation
The key is to compare pairs by concatenating in both possible orders and deciding which order yields a larger combined string.
Step 2: Recognize that sorting with a custom comparator based on concatenation comparisons guarantees optimal order
This approach ensures the final concatenation is lexicographically largest, unlike greedy or DP which do not handle pairwise ordering correctly.
Final Answer:
Option B -> Option B
Quick Check:
Custom comparator sorting is the standard solution for this problem [OK]

Quick Trick: Compare concatenations as strings to decide order [OK]

Common Mistakes:

MISTAKES

Assuming greedy pick of largest integer works
Using DP which is unnecessary
Brute force is correct but inefficient

Trap Explanation:

PITFALL

Greedy picking largest integer first seems intuitive but fails on cases like [3,30]. DP is overkill and not suited for ordering. Brute force is correct but impractical.

Interviewer Note:

CONTEXT

Tests if candidate can identify the correct pattern beyond brute force or naive greedy

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More Greedy Algorithms Quizzes

Which algorithmic approach guarantees an optimal solution for this problem?

Step 1: Understand the problem requires ordering numbers to maximize concatenation

Step 2: Recognize that sorting with a custom comparator based on concatenation comparisons guarantees optimal order

Final Answer:

Quick Check:

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